# 3.4 Motion with constant acceleration  (Page 8/10)

 Page 8 / 10

## Problems

A particle moves in a straight line at a constant velocity of 30 m/s. What is its displacement between t = 0 and t = 5.0 s?

150 m

A particle moves in a straight line with an initial velocity of 30 m/s and a constant acceleration of 30 m/s 2 . If at $t=0,x=0$ and $v=0$ , what is the particle’s position at t = 5 s?

A particle moves in a straight line with an initial velocity of 30 m/s and constant acceleration 30 m/s 2 . (a) What is its displacement at t = 5 s? (b) What is its velocity at this same time?

a. 525 m;
b. $v=180\phantom{\rule{0.2em}{0ex}}\text{m/s}$

(a) Sketch a graph of velocity versus time corresponding to the graph of displacement versus time given in the following figure. (b) Identify the time or times ( t a , t b , t c , etc.) at which the instantaneous velocity has the greatest positive value. (c) At which times is it zero? (d) At which times is it negative?

(a) Sketch a graph of acceleration versus time corresponding to the graph of velocity versus time given in the following figure. (b) Identify the time or times ( t a , t b , t c , etc.) at which the acceleration has the greatest positive value. (c) At which times is it zero? (d) At which times is it negative?

a.

b. The acceleration has the greatest positive value at ${t}_{a}$
c. The acceleration is zero at ${t}_{e}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{t}_{h}$
d. The acceleration is negative at ${t}_{i}\text{,}{t}_{j}\text{,}{t}_{k}\text{,}{t}_{l}$

A particle has a constant acceleration of 6.0 m/s 2 . (a) If its initial velocity is 2.0 m/s, at what time is its displacement 5.0 m? (b) What is its velocity at that time?

At t = 10 s, a particle is moving from left to right with a speed of 5.0 m/s. At t = 20 s, the particle is moving right to left with a speed of 8.0 m/s. Assuming the particle’s acceleration is constant, determine (a) its acceleration, (b) its initial velocity, and (c) the instant when its velocity is zero.

a. $a=-1.3{\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ ;
b. ${v}_{0}=18\phantom{\rule{0.2em}{0ex}}\text{m/s}$ ;
c. $t=13.8\phantom{\rule{0.2em}{0ex}}\text{s}$

A well-thrown ball is caught in a well-padded mitt. If the acceleration of the ball is $2.10\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}{\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ , and 1.85 ms $\left(1\phantom{\rule{0.2em}{0ex}}\text{ms}={10}^{-3}\phantom{\rule{0.2em}{0ex}}\text{s}\right)$ elapses from the time the ball first touches the mitt until it stops, what is the initial velocity of the ball?

A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of $6.20\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}{\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ for $8.10\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−}4}\phantom{\rule{0.2em}{0ex}}\text{s}$ . What is its muzzle velocity (that is, its final velocity)?

$v=502.20\phantom{\rule{0.2em}{0ex}}\text{m/s}$

(a) A light-rail commuter train accelerates at a rate of 1.35 m/s 2 . How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of 1.65 m/s 2 . How long does it take to come to a stop from its top speed? (c) In emergencies, the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency acceleration in meters per second squared?

While entering a freeway, a car accelerates from rest at a rate of 2.04 m/s 2 for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car travel in those 12.0 s? To solve this part, first identify the unknown, then indicate how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, check your units, and discuss whether the answer is reasonable. (d) What is the car’s final velocity? Solve for this unknown in the same manner as in (c), showing all steps explicitly.

a.

b. Knowns: $a=2.40\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2},t=12.0\phantom{\rule{0.2em}{0ex}}\text{s,}\phantom{\rule{0.2em}{0ex}}{v}_{0}=0\phantom{\rule{0.2em}{0ex}}\text{m/s}$ , and ${x}_{0}=0\phantom{\rule{0.2em}{0ex}}\text{m}$ ;
c. $x={x}_{0}+{v}_{0}t+\frac{1}{2}a{t}^{2}=\frac{1}{2}a{t}^{2}=2.40\phantom{\rule{0.2em}{0ex}}\text{m/}{\text{s}}^{2}{\left(12.0\phantom{\rule{0.2em}{0ex}}\text{s}\right)}^{2}=172.80\phantom{\rule{0.2em}{0ex}}\text{m}$ , the answer seems reasonable at about 172.8 m; d. $v=28.8\phantom{\rule{0.2em}{0ex}}\text{m/s}$

identify the magnitude and direction a vector quantity
Identify work done on an inclined plane given at angle to the horizontal
DOLLY
formula for Velocity
what is the value of x 6yx7y
what is the formula for frictional force
I believe, correct me if I am wrong, but Ffr=Fn*mu
Grant
frictional force ,mathematically Fforce (Ffr) =K∆R where by K stands for coefficient of friction ,R stands for normal force/reaction NB: R = mass of a body ( m) x Acc.due gravity (g) The formula will hold the meaning if and only if the body is relatively moving with zero angle (∅ = 0°C)
Boay
What is concept associated with linear motion
what causes friction?
Elijah
uneven surfaces cause friction Elijah
Shii
rough surfacea
Grant
what will happen to vapor pressure when you add solute to a solution?
how is freezing point depression different from boiling point elevation?
shane
how is the osmotic pressure affect the blood serum?
shane
what is the example of colligative properties that seen in everyday living?
shane
What is motion
moving place to place
change position with respect to surrounding
to which
to where ?
the phenomenon of an object to changes its position with respect to the reference point with passage of time then it is called as motion
Shubham
it's just a change in position
festus
reference point -it is a fixed point respect to which can say that a object is at rest or motion
Shubham
yes
Shubham
A change in position
Lily
change in position depending on time
bassey
Is there any calculation for line integral in scalar feild?
what is thrust
when an object is immersed in liquid, it experiences an upward force which is called as upthrust.
Phanindra
@Phanindra Thapa No, that is buoyancy that you're talking about...
Shii
thrust is simply a push
Shii
it is a force that is exerted by liquid.
Phanindra
what is the difference between upthrust and buoyancy?
misbah
The force exerted by a liquid is called buoyancy. not thrust. there are many different types of thrust and I think you should Google it instead of asking here.
Sharath
hey Kumar, don't discourage somebody like that. I think this conversation is all about discussion...remember that the more we discuss the more we know...
festus
thrust is an upward force acting on an object immersed in a liquid.
festus
uptrust and buoyancy are the same
akanbi
Shii
a Thrust is simply a push
Shii
the perpendicular force applied on the body
Shubham
thrust is a force of depression while
bassey
what is friction?
MFON
while upthrust is a force that act on a body when it is fully or partially submerged in a liquid
bassey
mathematically upthrust (u) = Real weight (wr) - Apparent weight (wa) u = wr- wa.
Boay
friction is a force which opposes relative motion.
Boay
how did astromers neasure the mass of earth and sun
wats the simplest and shortest formula to calc. for order of magnitude
papillas
Distinguish between steamline and turbulent flow with at least one example of each
what is newtons first law
It state that an object in rest will continue to remain in rest or an object in motion will continue to remain in motion except resultant(unbalanced force) force act on it
Gerald
Thanks Gerald Fokumla
Theodore
Gerald
it states that a body remains in its state of rest or uniform motion unless acted upon by resultant external force.
festus
it that a body continues to be in a state of rest or in straight line in a motion unless there is an external force acting on it
Usman
state's that a body will continue to maintain it present state of or of uniform unless it's being called upon by an external force
bassey
derive the relation above
formula for find angular velocity
w=v^2/r
Eric
v=wr>2
bassey
Why satellites don't fall on earth? Reason?
because space doesn't have gravity
Evelyn
satellites technically fall to earth but they travel parallel to earth so fast that they orbit instead if falling(plus the gravity is also weaker in the orbit). its a circular motion where the centripetal force is the weight due to gravity
Kameyama